M4maths Previous Puzzles

17 Feb 2016 Find the height and volume

A right pyramid stands on a rectangular base whose sides are 24 cm and 18 cm and each of the slant edge is 17 cm. Find the height and the volume of the pyramid.

OPtion

1) 12 cm and 1252 cm^3
2) 12 cm and 1164 cm^3
3) 10 cm and 1164 cm^3
4) 10 cm and 1254 cm^3
5) 6 cm and 1450 cm^3
6) 6 cm and 1152 cm^3
7) 6 cm and 1120 cm^3
8) 8 cm and 1152 cm^3
9) 8 cm and 1164 cm^3
10)8 cm and 1252 cm^3

Solution

By using figure
AB = 25 cm (base one side)
AD = 18 cm (base other side)
AS = 17 cm (slant edge)
Now
AO = Sqrt (AP^2 + OP^2) = Sqrt (9^2 + 12^2) = 15 cm (O is base centre and P is AD centre)
AS^2 = AO^2 + OS^2 (S is top point of pyramid)
then OS = Sqrt 64 = 8
height = 8
Volume = 1/3*18*24*8 = 1152 cm^2
Option 8)

Correct Option: 8 Best Solution (24)

Shagun Chaudhary   9 years AGO

base=1/2{18^2+24^2)^(1/2)
=15 cm
height=(17^2-15^2)
=8 cm
volume=(1/2)�18�24�8
=1152 cm^3

Like? Yes (2) | No   

Devendra Marghade   9 years AGO

Using Pythagoras theorem at base :
Given Base length=24, breadth=18, If Base diagonal=x
Then x^2=24^2 + 18^2, x^2=900, x=30
Considering 2nd right angled triangle with sides x/2, height(h) and slant edge=17
So 17^2 =15^2 + h^2, h^2=64 or h=8
Volume of the pyramid=Base length*Base breadth*height/3= (24*18*8)/3 =1152
Option 8) height=8 cm ,Volume=1152 cm^3

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MRITUNJAY   9 years AGO

height is 8 cm
volume of pyramid is (b*h)/3
=(24*18*8)/3=1152 cm^3
option 8

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Ravi   9 years AGO

height 8 by pythagoras
volume= 1/3(length*width*height)

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Ankita   9 years AGO

using hypotenous theorem we calculate height and volume has a simple formula 1/3area*height

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Maneesh Gupta   9 years AGO

b=1/2{18^2+24^2)^(1/2)
=15 cm
h=(17^2-15^2)
=8 cm
v=(1/2)�18�24�8
=1152 cm^3

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sanjeet kumar   9 years AGO

Since, height is given by root under (17^2 - 15^2) =8cm
And volume =l*w*h/3

Like? Yes (2) | No (1)  

Bablu patel   9 years AGO

first find diagonal of rectangle 18^2+24^2=900^1/2=30
hight will be measure from half of diagonal=15
hight=17^2-15^2=68^1/2=8
volume =l*h*w/3
=24*18*8/3
=1152

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GOURANGA SUNDAR MANDAL   9 years AGO

diagonal of the base rectangle is sqr root of(24^2 +18^2)=30
so the height of the pyramid is sqr root of (17^2-15^2)=8
so height of the pyramid is 8 cm..
the volume of the pyramid is (24*18*8)/3=1152 cm^3
so option 8 is correct answer

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UMANG RASTOGI   9 years AGO

sqrt.18^2+24^2=30
30/2=15
sqrt.17^2-15^2=8
hight=8;

volume=1/3*8*18*24=1152

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Gaurab Kumar Jha   9 years AGO

by applying pythagorus theorum
height of pyramid = 8
voume = l*b*h/3

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Juned Akhtar   9 years AGO

from pythagorois theorem & volume of pyramid formula = LBH/3

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sachin sawant   9 years AGO

diagonal of react=18^2+24^2=30cm
Height of pyramid=17^2-15^2=8cm
Volume=1/3area of base*h
=1/3*24*18*8
=1152cm^3
And option8

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ayushi   9 years AGO

volume of pyramid =1/3*area of base*height
height =8
area=24*18
volume =1/3*24*18*8=1152

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Priya jhunjhunwala   9 years AGO

we have to draw the fig carefully then by applying pythagorus teorem we will get the value of height i.e, h=8cm and volume will be (1/3) *area * height

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Saleel Kulkarni   9 years AGO

For the height of the pyramid, consider the a right angled triangle first. The hypotenuse is the slant edge = 17, the height is unknown whereas the base is half the diagonal of the rectangle. The length of the diagonal = sqrt(24^2 + 18^2)/2 = 15
So the by Pythagoras theorem, height of the pyramid = 8 cm.
Now volume of the pyramid = (length*breadth*height)/3=1152 cm^3
Option 8

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N.Vennela Rani   9 years AGO

height=8cm
volume=1152cm^3
by using formula v=(1/3)Ah

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Divyani gupta   9 years AGO

height of pyramid= sh2=h2+w2
h2=sh2-w2
volume=lwh/3

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Prakash Panda   9 years AGO

lwh/3 formula

using dis we can get h=8 n volume =1152 cm^3

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Siddharth Jain   9 years AGO

l = 24
w =18
slant height s = 17
rectangular base diagonal d = 30
so,
h^2 = s^2-(d/2)^2 = 64
h = 8 cm ANSWER

Volume of Pyramid = (lwh) / 3
= 1152 cm^3 ANSWER

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Mukund Manohar   9 years AGO

Diagonal (d) of rectangular base is
sq.root(d)=sq.root(24) + sq.root(18)
=576+324 =900
d=30 cm
Now,height (h) of pyramid is
sq.root(17)=sq.root(h) + sq.root(15),because diagonals of a rectangle bisect each other,so 30/2=15
289=sq.root(h) + 225
sq.root(h)=64
h=8 cm
Volume of pyramid=1/3 *24*18*8
=1152 cm^3

Like? Yes | No (1)  

sugayathri   9 years AGO

(17^2) - (900/2)^2 =8cm

volume of pyramid = 1/3ah

= 1/3*24*18*8

= 1152cm^3

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Rajeev teja   9 years AGO

Volume=a×b×h÷3
h=height
a,b= length and breadth of rectangle

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Jamil Ahmed   9 years AGO

Diagonal of the base = sqrt of (24^2 + 18^2) cm = 30 cm

So, height of the pyramid = sqrt of {17^2 + (30/2)^2} cm = 8 cm.

Therefore, volume of the pyramid = 24*18*8/3 cm^3 = 1152 cm^3.

Like? Yes | No (1)